From what I can see, you’re asking a 5 string to be a panacea bass, whereas, you don’t look for this in a 4 string, at least according to the above, bold paragraph section.
However, in answer to how do you find ‘the one’ 5 stringer; try as many as you need to until you find it, remembering what it was about the previous ones that weren’t right. It may be a compromise at the end of the day (as you already realise). If sticking with a 5 is where you want to go, you’ll probably want to try Sadowsky, Ibanez, Sandberg & Yamaha at least, but I wouldn’t get hung up on the pickup configuration given how differently voiced just soapbars can be. Perhaps, as has been suggested, a custom instrument may be a way forward, but don’t count on that. I wish you luck, @TheGreek and don’t beat yourself up about the search, it’s meant to be fun surely?
Finally, I have a question, albeit largely rhetorical - is there a ‘the one’ bass for everyone? I suspect not and the for sale section on this hallowed forum alone supports that suspicion. There is a ‘the one’ bass for some players certainly and they fit into a couple of types (I’m sure there are other groups, however). First, those who learnt to play back when choice was very limited, found something that worked and that bass is now like a pair of comfortable (insert clothing simile of your choosing) and change would be anathema to their being. Then there are those lucky folk have found a level and style of playing that they’re completely happy with and have a bass that suits that. They’ll occasionally dabble with new techniques and try something new gear-wise, but they’ll come back to old faithful quite quickly (NB of course some ‘fall off the wagon’ and are down the gear rabbit hole with the rest of us). Others are still finding their way as players and their gear requirements change with that evolution (I count myself in this group and I don’t think there is a ‘the one’ for me, probably more a ‘the four’ and I’m homing in on the last of that quiver). Finally, there are the bass junkies, beloved by the musical instrument industry. There isn’t a ‘the one’ for them and they’ll try anything and everything, new, old, weird, you name it. Vive la difference!